Abstract

We prove new results on evasiveness of monotone graph properties by extending the techniques of Kahn, Saks and Sturtevant [4]. For the property of containing a subgraph isomorphic to a fixed graph, and a fairly large class of related n-vertex graph properties, we show evasiveness for an arithmetic progression of values of n. This implies a 1/2n2 - O(n) lower bound on the decision tree complexity of these properties.

We prove that properties that are preserved under taking graph minors are evasive for all sufficiently large n. This greatly generalizes the evasiveness result for planarity [1]. We prove a similar result for bipartite subgraph containment.